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• W2097108250 abstract "We consider the problem of estimating Shannon's entropy H from discrete data, in cases where the number of possible symbols is unknown or even countably infinite. The process, a generalization of Dirichlet process, provides a tractable prior distribution over the space of countably infinite discrete distributions, and has found major applications in Bayesian non-parametric statistics and machine learning. Here we show that it provides a natural family of priors for Bayesian entropy estimation, due to the fact that moments of the induced posterior distribution over H can be computed analytically. We derive formulas for the posterior mean (Bayes' least squares estimate) and variance under Dirichlet and process priors. Moreover, we show that a fixed Dirichlet or process prior implies a narrow prior distribution over H, meaning the prior strongly determines the entropy estimate in the under-sampled regime. We derive a family of continuous measures for mixing processes to produce an approximately flat prior over H. We show that the resulting Pitman-Yor Mixture (PYM) entropy estimator is consistent for a large class of distributions. Finally, we explore the theoretical properties of the resulting estimator, and show that it performs well both in simulation and in application to real data." @default.
• W2097108250 created "2016-06-24" @default.
• W2097108250 creator A5026150866 @default.
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• W2097108250 date "2014-01-01" @default.
• W2097108250 modified "2023-09-24" @default.
• W2097108250 title "Bayesian entropy estimation for countable discrete distributions" @default.
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• W2097108250 doi "https://doi.org/10.5555/2627435.2697056" @default.
• W2097108250 hasPublicationYear "2014" @default.
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